Which one of the following could be true?

Irina on September 17, 2019

@Ryan-Mahabir,

This game requires us to determine the order of seven musicians - L M N O P S T. The following rules apply:

(1) L must perform earlier than N
L< N

We can infer that N cannot perform 1st, and L cannot perform 7th.

(2) M must perform earlier than T
M
We can infer that M cannot be 7th, and T cannot be 1st.

(3) There must be exactly one performance between O & L

L _ O or O_L

(4) There must be exactly one performance between M & P

M_P or P_M

(5) P must perform 1st or 7th.

P -1 v 7

So we can infer that M must perform 3 or 5 per rule (4).

Let's diagram all the rules together:

___ ___ ___ ___ ___ ___ __
1 2 3 4 5 6 7
/P /M /M /P
~N ~L
~T

Let's look at the answer choices:

(A) M performs 4th.
Impossible. M must be 3d or 4th per rules (3) and (5).

(B) N performs 1st.
Impossible. N cannot be #1 per rule (1).

(C) O performs 5th.
Since L cannot be 7th, the only way O could be 5th is if L is 3d but then there is no place left for M with both 3d and 5th spot taken, hence this scenario is also impossible.

(D) S performs 7th.
If S performs 7th, P must be 1st, M must be 3d, Then L & O could be #2 and #4, and N & T #5 and #6. Since this scenario complies with all the rules, (D) is the correct answer.

P L M O N T S
1 2 3 4 5 6 7

(E) T performs 2d.

Impossible. If T performs 2d, M must perform 1st per rule (2) but per rules (4) (5), only one performance can separate M & P and P must be 1st or 7th. If M is #1, it will force P into #3 slot, which violates rule (5). We can thus conclude that T cannot be #2.

M T P
1 2 3 4 5 6 7

Let me know if this makes sense and if you have any further questions.